I did Kansas City last year, saw the Sox win in 13 innings. Here are my notes:
1. There are two nice areas in Central KC. There's a "downtown", part of which is called the Power and Light District, and there's an area called the "Country Club Plaza", which as far as I can tell is just a second downtown. They are not right next to each other, but one is walkable from the other: it's roughly the distance between River North and the South Loop in Chicago, maybe a bit closer.
Jack Stack, one of the legendary BBQ places, is inbetween the two, closer to Country Club Plaza. North of downtown, there's this area by the river that has a steamboat museum, where they raised a sunken steamboat and put all the stuff inside on display. I thought it was super cool.
2. There is another area called 18th and Vine, which is where all of the jazz was in the 1920's. It's pretty far from downtown - I did walk there from downtown, but it was a 30-45 minute walk through some rough-looking areas. This is where the Negro League Museum was, which was amazing, and it's where Arthur Bryant's, the other legendary BBQ place, is. If you only visit two things in Kansas City, visit the Negro League Museum and Arthur Bryant's.
3. Kauffman Stadium is really nice, but it's in the middle of nowhere outside of town. You will need to either rent a car, or cab it: I think the cab fare is like $20. Royals fans are nastier than you'd expect.
"Hope...may be indulged in by those who have abundant resources...but its nature is to be extravagant, and those who go so far as to stake their all upon the venture see it in its true colors only when they are ruined."